General methods of elliptic minimization

General methods of elliptic minimization We provide general methods in the calculus of variations for the anisotropic Plateau problem in arbitrary dimension and codimension. Given a collection of competing “surfaces” that span a given “bounding set” in an ambient metric space, we produce one minimizing an elliptic area functional. The collection of competing surfaces is assumed to satisfy a set of geometrically-defined axioms. These axioms hold for collections defined using any combination of homological, cohomological or linking number spanning conditions. A variety of minimization problems can be solved, including sliding boundaries. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Calculus of Variations and Partial Differential Equations Springer Journals

General methods of elliptic minimization

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany
Subject
Mathematics; Analysis; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics
ISSN
0944-2669
eISSN
1432-0835
D.O.I.
10.1007/s00526-017-1217-6
Publisher site
See Article on Publisher Site

Abstract

We provide general methods in the calculus of variations for the anisotropic Plateau problem in arbitrary dimension and codimension. Given a collection of competing “surfaces” that span a given “bounding set” in an ambient metric space, we produce one minimizing an elliptic area functional. The collection of competing surfaces is assumed to satisfy a set of geometrically-defined axioms. These axioms hold for collections defined using any combination of homological, cohomological or linking number spanning conditions. A variety of minimization problems can be solved, including sliding boundaries.

Journal

Calculus of Variations and Partial Differential EquationsSpringer Journals

Published: Aug 3, 2017

References

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